Question

solve for x : (1/x+1 ) + (2/ x + 1 ) = ( 4/x+ 4 )

Answer 1

★Question:

$Solve\:for\:x ->\frac{1}{x+1} + \frac{2}{x+1} = \frac{4}{x+4}$

★Solution:

$\frac{1}{x+1} + \frac{2}{x+1} = \frac{4}{x+4}\\ \\ \\ \frac{(1+2)}{x+1} = \frac{4}{x+4}\\ \\ \\ \frac{3}{x+1} = \frac{4}{x+4}\\ \\ \\ by\: cross\: multiplication\\ \\ \\ 3(x+4) = 4(x+1) \\ \\ \\ 3x+12 = 4x+4\\ \\ \\ 4x-3x = 12-4\\ \\ \\ {\pink{\boxed{x = 8}}}$

Answer 2

Answer:

★ Hence, we get, the value of x = 8

Step-by-step explanation:

★ Given,

➡ [1 / (x + 1)] + [2 / (x + 1)] = 4 / (x + 4)

★ To Find :

➡ Value of x

★ Solution :

[1 / (x + 1)] + [2 / (x + 1)] = 4 / (x + 4)

• Since, the denominator of the terms of LCM is same, we can add them.

➡ (1 + 2) / (x + 1) = 4 / (x + 4)

➡ 3 / (x + 1) = 4 / (x + 4)

• On cross - multiplication, we get,

➡ 3(x + 4) = 4(x + 1)

➡ 3x + 12 = 4x + 4

➡ 4x - 3x = 12 - 4

➡ x = 8

Hence, we get, the value of x = 8

★ Verification :

For verification, we can directly apply the value of x in the given expression.

[1 / (x + 1)] + [2 / (x + 1)] = 4 / (x + 4)

➡ [1 / (8 + 1)] + [2 / (8 + 1)] = 4 / (8 + 4)

➡ 1 / 9 + 2 / 9 = 4 / 12

➡ 3 / 9 = 4 / 12

On cross multiplication, we get,

➡ 12 × 3 = 4 × 9

➡ 36 = 36

LHS = RHS

Hence, verified.